16%20-%20Applications%20of%20Integration

16%20-%20Applications%20of%20Integration - PROBLEMS(1 16...

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PROBLEMS 16 - APPLICATIONS OF INTEGRATION Page 1 ( 1 ) Find the area of the region bounded by the circle x 2 + y 2 = r 2 . [ Ans: π r 2 ] ( 2 ) Find the area of the region bounded by y = x 2 - 5x + 4 and X-axis. 2 9 : Ans ( 3 ) Find the area of the region enclosed by y 2 = 8x and x + y = 0. 3 32 : Ans ( 4 ) Find the area of the region between the circles, x 2 + y 2 = 4 and x 2 + y 2 = 4x. π 3 2 3 8 : Ans - ( 5 ) Prove that the area of the region bounded by y = 4x - x 2 and X-axis is 3 32 . ( 6 ) Find the volume of the solid obtained by revolution of portion of the ellipse 1 b y a x 2 2 2 2 = + on right hand semi plane of Y-axis about Y-axis. π b a 3 4 : Ans 2 ( 7 ) If the region bounded by y 2 = 8x from its vertex to x = 2 is rotated about X-axis, find the volume of the solid generated. [ Ans: 16 π ] ( 8 ) Prove that the volume of the solid generated by revolving the region bounded by y = x 2 + 1 and y = 2x + 1 about X-axis is 15 104 π .
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PROBLEMS 16 - APPLICATIONS OF INTEGRATION Page 2 ( 9 ) Find the volume of the right circular cone having semi-vertical angle α and radius of base equal to r.
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